To study the effect of parity-violation on the rate of complexity growth, by using "Com-plexity=Action" conjecture, we find the complexity growth rates in different solutions of the chiral theory of Topologically Massive Gravity (TMG) and parity-preserving theory of New Massive Gravity (NMG). Using the results, one can see that decreasing the parameter µ, which increases the effect of Chern-Simons term and increases chirality, would increase the rate of growth of complexity. Also one can observe a stronger correlation between complexity growth and temperature rather than complexity growth and entropy. At the end we comment on the possible meaning of the deforming term of chiral Liouville action for the rate of complexity growth of warped CFTs in the Tensor Network Renormalization picture.

By using AdS/CFT, we study the critical electric field, the Schwinger pair creation rate and the potential phase diagram for the quark and anti quark in four confining supergravity backgrounds which are the Witten QCD, the Maldacena-Nunez, the Klebanov-Tseytlin and the Klebanov-Strassler models. We compare the rate of phase transition in these models and compare it also with the conformal case. We then present the phase diagrams of the entanglement entropy of a strip in these geometries and find the predicted butterfly shape in the diagrams. We find that the phase transitions have higher rate in WQCD and KT relative to MN and KS. Finally we show the effect of turning on an additional magnetic field on the rate of pair creation by using the imaginary part of the Euler-Heisenberg effective Lagrangian.The results is increasing the parallel magnetic field would increase the pair creation rate and increasing the perpendicular magnetic field would decrease the rate.arXiv:1506.08557v3 [hep-th]

In this work we study how entanglement of purification (EoP) and the new quantity of "complexity of purification" are related to each other using the E P = E W conjecture. First, we consider two strips in the same side of a boundary and study the relationships between the entanglement of purification of this mixed state and the parameters of the system such as dimension, temperature, length of the strips and the distance between them. Next, using the same setup, we introduce two definitions for the complexity of mixed states, complexity of purification (CoP) and the interval volume (VI). We study their connections to other parameters similar to the EoP case. Then, we extend our study to more general examples of BTZ black holes solution in massive gravity, charged black holes and multipartite systems. Finally, we give various interpretations of our results using resource theories such as LOCC and also bit thread picture.